5w^2-12w-391=0

Solution for 5w^2-12w-391=0 equation:

5w^2-12w-391=0

a = 5; b = -12; c = -391;
Δ = b2-4ac
Δ = -122-4·5·(-391)
Δ = 7964
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$w_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$w_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

The end solution:

$\sqrt{\Delta}=\sqrt{7964}=\sqrt{4*1991}=\sqrt{4}*\sqrt{1991}=2\sqrt{1991}$
$w_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-12)-2\sqrt{1991}}{2*5}=\frac{12-2\sqrt{1991}}{10}
$
$w_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-12)+2\sqrt{1991}}{2*5}=\frac{12+2\sqrt{1991}}{10}
$